Q. If one root of equation $x^{2} + ax + 12 = 0$ is 4 while the equation $x^{2} + ax + b = 0$ has equal roots, then the value of $b$ is
A) $\frac{4}{49}$
B) $\frac{49}{4}$
C) $\frac{7}{4}$
D) $\frac{4}{7}$
Explanation
(b)
Since, 4is a root of $x^{2} + ax + 12 = 0$
$\therefore 16 + 4a + 12 = 0\ \Rightarrow a = - 7$
Let the roots of the equation $x^{2} + ax + b = 0$ be $\alpha$ and $\alpha$
$\therefore 2\alpha = - a$
$\Rightarrow \ \alpha = \frac{7}{2}$
And $\alpha.\alpha = b$
$\Rightarrow \ \left( \frac{7}{2} \right)^{2} = b$
$\Rightarrow b = \frac{49}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.